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fundamental difference between a polynomial function and an exponential function?
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Exponential relationship!
"The" exponential function is ex. A more general exponential function is any function of the form AeBx, for any non-xero constants "A" and "B". Alternately, Any function of the form CDx (for constants "C" and "D") would also be considered an exponential function. You can change from one form to the other.
That means that the growth is equal to, or similar to, an exponential function, which can be written (for example) as abx, for constants "a" and "b". One characteristic of exponential growth is that the function increases by the same percentage in the same time period. For example, it increases 5%, or equivalently by a factor of 1.05, every year.